A canonical structure theorem for finite joining-rank maps

A numerical isomorphism invariant,joining-rank, was introduced in [1] as a quantitative generalization of Rudolph’s property of minimal selfjoinings. Therein, a structure theory was developed for those transformationsT whose joining-rank, jr (T), is finite. Here, we sharpen the theorem and show it to be canonical: If jr (T)<∞ then there is a unique triple 〈e, p, S〉 wheree andp are natural numbers andS is a map with minimal self-joinings, such thatT is ane-point extension ofS ^P. Furthermore, the producte·p equals the joining-rank ofT. This theorem applies to any finite-rank mixing map, since for such maps the rank dominates the joining-rank. Another corollary is that any rank-1 transformation which is partial-mixing has minimal self-joinings. This partially answers a question of [3]. Partially supported by a National Science Foundation Postdoctoral Research Fellowship.     

On a deception game with three boxes

This paper clarifies the status of a deception game posed by Spencer. We show the value of this game is zero.     

Comparison of singlet methylene removal rates by group IV hydrides

The technique of laser flash photolysis/laser absorption has been used to obtain an absolute removal rate constant of (3.85 ± 0.18) × 10^?10 cm³ molecule^?1 s^?1 for singlet methylene, ¹CH₂ (ã¹A₁), with germane (GeH₄) at ambient temperature. The removal rate constant is compared with the values for methane (CH₄) and silane (SiH₄) which have been determined previously. © 1995 John Wiley & Sons, Inc.     

Asymptotic analysis of a model for substitutional-interstitial diffusion

A substitutional-interstitial model for impurity diffusion in semi-conductors is discussed. In particular we consider a surface-source problem and obtain asymptotic solutions in the limit of the surface concentration of impurity being much greater than the equilibrium vacancy concentration. In the absence of vacancy generation, a double error function impurity curve is obtained. These double profiles reproduce some of the qualitative features of diffusion in many III–V semiconductor systems. We also discuss how vacancy generation modifies the analysis and show that in the limit of high vacancy generation, the problem becomes one of linear diffusion with the diffusion curves then being single error function complements.     

Infrared Laser Ablation Sample Transfer for MALDI and Electrospray

We have used an infrared laser to ablate materials under ambient conditions that were captured in solvent droplets. The droplets were either deposited on a MALDI target for off-line analysis by MALDI time-of-flight mass spectrometry or flow-injected into a nanoelectrospray source of an ion trap mass spectrometer. An infrared optical parametric oscillator (OPO) laser system at 2.94 μm wavelength and approximately 1 mJ pulse energy was focused onto samples for ablation at atmospheric pressure. The ablated material was captured in a solvent droplet 1–2 mm in diameter that was suspended from a silica capillary a few millimeters above the sample target. Once the sample was transferred to the droplet by ablation, the droplet was deposited on a MALDI target. A saturated matrix solution was added to the deposited sample, or in some cases, the suspended capture droplet contained the matrix. Peptide and protein standards were used to assess the effects of the number of IR laser ablation shots, sample to droplet distance, capture droplet size, droplet solvent, and laser pulse energy. Droplet collected samples were also injected into a nanoelectrospray source of an ion trap mass spectrometer with a 500 nL injection loop. It is estimated that pmol quantities of material were transferred to the droplet with an efficiency of approximately 1%. The direct analysis of biological fluids for off-line MALDI and electrospray was demonstrated with blood, milk, and egg. The implications of this IR ablation sample transfer approach for ambient imaging are discussed.     

Fourier transform infrared matrix-isolation analysis of acetaldehyde fragmentation products after charge exchange with Ar•+ under varied ionization density conditions

The products of the Ar^?+ charge exchange ionization of acetaldehyde have been isolated and compared with related photoionization results and computational work. Acetaldehyde has been used to assess the effect of varied ion density in the ionization region of the electron bombardment matrix isolation apparatus. The amount of acetaldehyde destruction has been measured for constant gas‐sample composition and constant ionization current for two anode geometries: a pin anode and a plate anode. For the same ionization current, a pin‐shaped anode demonstrates higher precursor molecule destruction efficiency (85%) than the plate‐shaped anode (30%), resulting in substantial effect on the yield and quantity of isolated products. When the plate anode is used, the observed infrared products correspond to matrix‐isolated carbon monoxide (CO), methane (CH₄), ketene (CH₂CO), ethynyloxy radical (HCCO), formyl radical (HCO^?), acetyl radical (CH₃CO^?), vinyl alcohol (H₂C = CH‐OH), and cationic proton‐bound dimer, Ar₂H⁺. When the pin anode is used, the same products are observed with different relative proportions and new absorption features corresponding to dicarbon monoxide (CCO) and methyl radical (CH₃^?) are observed. The surprising observation of infrared absorptions corresponding to vinyl alcohol along with low yield of products anticipated through the analysis of photoelectron–photoionization coincidence measurements suggests that the initially formed fragmentation products are able to further react within the matrix‐isolation environment to influence observed product yields. Related experiments, using the isotopomer CD₃CHO, suggest that the observed products are formed via radical–radical reactions that occur under the high pressure conditions of the matrix isolation environment. Copyright © 2011 John Wiley & Sons, Ltd.     

Mononuclear homoleptic allyl complexes of the first row transition metals: species with unusual metal electronic configurations

A number of evanescent unsubstituted homoleptic allyl derivatives M(C(3)H(5))(n) of the first row transition metals have been reported in the literature. In addition, the much more thermally stable silylated derivatives M[C(3)H(3)(SiMe(3))(2)](2) (M = Cr, Fe, Co, Ni) are reported to survive vacuum sublimation without significant decomposition. In this connection, the complete series of homoleptic allyl derivatives M(C(3)H(5))(n) (n = 2, 3; M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni) have been studied theoretically using density functional theory. In most of the lowest energy predicted M(C(3)H(5))(n) structures all of the allyl groups are bonded as trihapto η(3)-C(3)H(5) ligands and the metals have considerably less than the normally favored 18-electron configuration. Such ligands can be considered formally as bidentate ligands with the metal atom connected to the centers of the two C-C bonds of the η(3)-C(3)H(5) group. The later transition metal diallyls M(C(3)H(5))(2) (M = Cr, Mn, Fe, Co, Ni) form two stereoisomers of similar relative energies, namely the C(2h) staggered isomer and the C(2v) eclipsed isomer with the orientation of the η(3)-C(3)H(5) groups corresponding to square planar metal coordination of the bidentate η(3)-C(3)H(5) ligands. The staggered and eclipsed Ni(C(3)H(5))(2) isomers have been observed experimentally by NMR. Less symmetrical M(C(3)H(5))(2) structures are found for the earlier transition metals Sc, Ti, and V in which the orientation of the allyl groups corresponds to tetrahedral metal coordination. The triallylmetal derivatives M(C(3)H(5))(3) are predicted to be thermodynamically viable with respect to allyl loss to give the corresponding diallylmetal derivatives, except for triallylnickel. The lowest energy Ni(C(3)H(5))(3) structure has two trihaptoallyl ligands and one monohaptoallyl ligand, whereas the lowest energy Mn(C(3)H(5))(3) structures have only one trihaptoallyl ligand and two monohaptoallyl ligands. Otherwise, the M(C(3)H(5))(3) complexes have structures with three trihaptoallyl ligands corresponding formally to octahedral metal coordination. The M(C(3)H(5))(3) complexes (M = Cr, Co) thus correspond to a well-known series of "classical" octahedral coordination complexes, namely, those of the d(3) Cr(III) and the d(6) Co(III), respectively.     

A general route for the synthesis of functional, protein-based hydrogel microspheres using tailored protein charge

pH-induced protein aggregation facilitated the formation of nucleation centers for the chain growth polymerization of hydrogel microspheres.     

Confined PFSA-zeolite composite membrane for self-humidifying fuel cell

Perfluorosulfonic acid (PFSA) polyelectrolyte confined in subnanoliter volume within zeolite cladded walls exhibits higher glass transition temperature and excellent tolerance to high-temperature fuel cell operation under dry conditions, generating an order of magnitude higher power density than standard PEMFC.